It has been implied at times that the Doctor is rather like Superman - he's constantly holding back.
A non-canon description is found in the audio play When Death Comes to Time, in which Ace is being trained to become a Time Lord. One of her trials is to cross an underground lake without touching the deadly red liquid of the lake. She has to jump from one stalagmite to another, balancing precariously all the way.
She finally falls in and panics as the red liquid douses her. Her guide explains that the liquid is exactly the same as water, except in one regard: It is red. She realises that there is no danger at all. Her guide then asks her if, knowing that, she could still make herself cross the lake the hard way, by hopping across the stalagmites.
The Doctor is known to have astonishing potential abilities. He can sense effectively everything around him, he can end a politician's career with six words, he can freeze his enemies eternally in place as scarecrows. He can trap people in reflections, can make them immortal but trap them eternally. He can channel incredible amounts of psychic energy if it's available...but he tries not to. He's like a giant living in a world full of children - he daren't use anything like his actual strength, for fear of destroying those around him.
All the powers that he has displayed are likely to be part of a more general power set, but we don't know what that power set is. Likely we'll never know; likely we never could know.
All of which is a long way of saying "He has the powers that the plot demands, and doesn't use powers when the plot demands tension."